The topology of balls and Gromov hyperbolicity of Riemann surfaces

Jesús Gonzalo Pérez, Ana Portilla, José M Rodríguez +1

For each k > 0 we find an explicit function f_k such that the topology of S inside the ball B(p,r) is `bounded' by f_k(r) for every complete Riemannian surface (compact or noncompa…